I have a certain population U. The members x of U each either satisfy or don't satisfy a property p. That is, p(x) is either true or false for each x in U.
I want to get an estimate of the fraction of members of U that satisfy p. I do this by repeatedly sampling from U (with replacement) for some fixed time such as 60 seconds. (This is a computer program I'm talking about.)
After sampling n items, I conclude the proportion is the number of items I found for which p is true divided by n. Let f be this fraction (with 0 <= f <= 1).
That's all simple enough. What I want to know is whether I can establish (a reasonably tight) upper-bound, b, on the error of f.
I naively assumed that the error b would be the abs(f - f') where f' is the fraction calculated after n - 1 samples. From experimentation, I discovered this assumption was wrong.
Is there a way to get a reasonably tight bound b?